TA262

DMA 2980DYNAMIC MECHANICAL ANALYZER

Prepared by

Sujan E. Bin Wadud andRussell R. Ulbrich,TA Instruments, Inc.

Time-Temperature Superposition Tutorial ForAdvantage Software

TABLE OF CONTENTS

A Brief Introduction to Time-Temperature Superposition Principle . . . . . . . . . . . . . . . . . . . . 1

Programming a TTS Experiment on the DMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Test Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Creating the Frequency Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Viewing and Shifting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Viewing Data in Universal Analysis NT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Converting DMA 2980 Data File to TTS Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Shifting the TTS Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Analysis using WLF/Arrhenius Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Generating the Master Curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

A Brief Introduction to Time-TemperatureSuperposition Principle

The linear viscoelastic properties of polymers are dependent on both time andtemperature. A thorough description of the theories behind the inter-relationship oftime and temperature is beyond the scope of this tutorial. In general, however, therelaxation process of a polymer at a particular temperature will be enhanced atelevated temperatures, i.e. the relaxation times will be shorter at any highertemperature. In essence, the time-temperature superposition principle assumes thatby changing the temperature, the complete relaxation spectrum is affected by thesame degree. Hence, increasing the temperature shortens all relaxation times by thesame factor. There are some empirical relationships that deal with the dependenceof the enhancement or slowing down of the relaxation processes on the change intemperature. One should note that not all materials obey the time-temperaturesuperposition principle. The polymers that do obey are referred to as thermo-rheologically simple materials.

Usually, rheological measurements are made such that either the temperature or thefrequency/time is held constant while the other parameter is varied. In the case ofoscillation experiments in which the temperature is held constant and the frequencyor time is varied, the data spans over a two to four decade range in frequency/time.By repeating such tests over a number of temperatures, one obtains a set ofisothermal dependencies of, say, storage modulus (E’) or loss modulus (E’’) inshear versus frequency, ω. If the material is thermo-rheologically simple, then onecan shift any of the linear viscoelastic parameters, e.g. E’, E’’, J’, J’’, η ’, η ’’, orG(t), J(t), etc., along the time/frequency axis such that they are superimposed on oneanother to generate a master curve at a particular temperature.

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So, time-temperature superposition (TTS) makes it possible to characterize theviscoelastic properties of materials at various temperatures over an experimentallyconvenient time or frequency range. The curve shifting procedure creates a mastercurve that represents the time response of a material over a wide range oftimes/frequencies at a particular reference temperature. TTS can be used to obtainmaster curves from creep, stress relaxation and oscillations experiments. Thistutorial highlights the use of TTS for data obtained from oscillatory experiments intension.

Programming a TTS Experiment on the DMA 2980

It is necessary to ascertain what one would like to accomplish using TTS. Usually,the material under consideration will have a use temperature (or a range thereof),and an understanding of its properties at different time scales at this temperature isdesired. A reference temperature, Tr, is selected based on the use temperature andthe data at other temperatures is shifted to this reference temperature. To obtaininformation at higher frequencies or shorter times, frequency scans (stress relaxationor creep) should be performed at temperatures lower than Tr. To obtain informationat lower frequencies or longer times, frequency scans have to be performed attemperatures higher than Tr. For example, to get a description of PET for roomtemperature application over very long time scales, one should perform frequencysweeps within the temperature range of, say, 25°C to 200°C, and then pick 25°C asthe reference temperature.

A good starting point is to perform a temperature scan of the material at a single frequency toget an idea of the modulus–temperature and transition behavior. This provides a basis forthe temperature range to be covered on the DMA 2980 relative to the reference temperature.

Test Parameters

To run any TTS experiment with the Thermal Advantage NT software, first theclamp type and the program mode must be selected. This is done by either clicking

on or going to

Experimental _ Mode…

One may select any one of the following modes for experimentation for TTS andthen click :

• DMA Multi-Frequency• DMA Creep• DMA Stress Relaxation

The film tension clamp has been selected in this example.

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Fig. 1. Screen captureof the Mode selectionwindow in ThermalAdvantage NT.

There are procedure templates for TTS experiments in the Thermal Advantagesoftware. Based on the mode selected, one should select the appropriate procedureon the Summary page, as shown below:

Fig. 2. Screen captureof the Mode selectionwindow in ThermalAdvantage NT.

After selecting the procedure, click on .

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Now, the user has to enter the test parameters in the Procedure page, which isshown below in Fig. 3. Since TTS relies on linear viscoelastic information, it isimportant to select an amplitude such that the deformation is in the linear regime. Agood rule of thumb is that polymeric solids are linear up to 0.1% strain (or 0.001strain units). A strain lower than 0.1% is preferable†. To calculate the amplitudethat translates to the required strain, please refer to Chapter 6 of the DMA 2980Operators Manual.

Fig. 3. Screen captureof the Procudure pagein Thermal AdvantageNT.

Next, enter values in the fields for Start temperature, which is usually the lowesttemperature, and the Final temperature, i.e., the highest temperature to run thefrequency sweeps/creep/stress relaxation. A Temperature increment of 5°C isusually a well-sized step to get good overlapping in the various frequency scans.Refer to the “DMA 2980 Getting Started Guide” for preload force and force trackinformation, if needed. For most materials and sample dimensions, an Isothermalsoak time of 5 minutes is usually enough for homogeneous temperature distributionwithin the sample. When all the parameters have been entered, click on again.

Clicking on in the procedure page brings up the following window:

Fig. 4. Screen captureof the Advanced settingwindow. The datasampl ing interva lshould be set to 2.0sec/pt.

The data sampling interval should be set to 2 sec/pt for TTS experiments.

† For a detailed discussion of the linear viscoelastic region, see DMA 2980 Getting Started Guide.

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Again, on the procedure page, the post-test conditions can be set by clicking on which brings up the following window:

Fig. 5. Screen captureof the Post Testsettings window. Thedata sampling intervalshould be set to 2.0sec/pt.

These parameters control the state of the DMA 2980 after the experiment hasconcluded. To bring the system back to room temperature after the test iscompleted, enter the appropriate values in Return to temperature range fields asshown above. One may choose to keep the furnace open or closed after theexperiment by selecting the appropriate radio button, as shown above. It should benoted that while the oven is closed, the instrument tries to maintain the range oftemperatures. This could lead to unnecassary loss of cooling liquid. To allow therelaxation of any stresses that may be built up in the sample during the rapid cool-down, the clamp may be left in Float mode. When repeating a number of tests oneafter another, check the GCA Autofill box for convenience.

Creating the Frequency Table

The set of frequency values at which the material will be tested must be evenlyspaced over a log scale because viscoelastic data is interpreted on a log-log scale.Also, individual sweeps have to be performed with a wide enough range infrequencies so that there is ample overlap between the sweep data at differenttemperatures. Usually, a 3 decade span between the lowest and the highestfrequencies and a temperature increment of 5°C will lead to sufficient overlap in thedata. Press the “Frequency Table” tab on the procedure screen to get to thefollowing screen:

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Fig. 6. Screen captureof Frequency Table.Select the Log radiobutton and enter thetemperature range andthe points per decadesuch that the totalnumber of frequenciesis less than 28.

Select the Log radio button and enter the frequency range. A frequency range of100 to 0.1 Hz is adequate for any TTS experiment. Gathering data at frequenciesbelow 0.1 Hz will greatly lengthen the time of the experiment. For the field forPoints Per Decade field, a value of 5 is standard for most applications. In thisexample, three decades of frequncies are programmed (100 to 10, 10 to 1 and 1 to0.1 Hz) at 5 points per decade. These parameters will yield 15 points in eachfrequency sweep. When selecting the frequency range and points per decadeparameters, values must be chosen such that the total number of frequencies to bescanned does not exceed 28. One can also enter a discrete set of frequencies.

The lower the frequency, the longer are the times required for measurement. Hence, the totalduration of the test will be dominated by the time taken to measure low frequency values. Forthis reason, it is recommended that the range of frequencies be programmed starting with thehighest frequency and decreased to end with the lowest one.

Viewing and Shifting Data

This section deals with viewing multiplexed data generated by the DMA 2980 usingUniversal Analysis NT and shifting the data using the TTS Data Package. Theexample that follows uses a demonstration file that comes with Universal AnalysisNT, called Dma-pet.001 in the C:\TA\data\DMA directory.

Viewing Data in Universal Analysis NT

The raw data are typically viewed as frequency scans at different temperatures or astemperature scans at different frequencies using Universal Analysis NT. Examplesof both scenarios are shown here. Once the file C:\TA\Data\DMA\Dma-pet.001 has been selected, the following window enables one to select the signals

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and their axes.

Fig. 7. Screen captureof the opening of adata file in UniversalAnalysis NT.

Click on to bring up the following window and select the signals thatneed to be assigned to the different axes.

Fig. 8. Assigningsignals to differentaxes in UniversalAdvantage NT.

Selecting Frequency as the X signal brings up the following screen (Fig. 8). Figure9 shows the scenario in which temperature is plotted on the X axis.

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Fig. 9. Screen captureof Dma-pet.001 viewedwith Universal AnalysisNT. Frequency scans atdifferent temperatures(25¡C to 160¡C).

Fig. 10. Screencapture of Dma-pet.001 viewed withUniversal Analysis NT.Temperature scans atdifferent frequencies(0.1 Hz to 20 Hz).

Converting the DMA 2980 Data File to TTS Format

Once the data are plotted as shown above, the file has to be exported in text formatprior to shifting. To convert the file to the required text format, select the followingfrom the file menu:

File _ Export Data File _TTS Signals

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This is shown in the illustration below:

Fig. 11. Screencapture of exportingthe TTS Signals fromUniveral Analysis NT.

This will bring up the the window shown below in Fig. 8. All the signals areselected by default. Upon selecting the output signals to be exported, click on

.

Fig. 12. Screencapture o f theselection window forthe signals to beexported.

This brings up the following window, in which, a new filename may be entered.The program automatically assigns a “.txt” extention to the filename.

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Fig. 13. Exporting theTTS Signals fromUniveral Analysis NT.

When the desired name has been entered in the File name field, click on .

Shifting the TTS Data

Start the TTS Data Analysis package. This is found in the Windows Start menu asshown below:

_ Programs _ TA Thermal Advantage _ TTS Data Analysis

Fig. 14. Starting theData Analysis software.

Once TTS Data Analysis is running, open the text file that was created usingUniversal Analysis using

File _ Open

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Fig. 15. Opening theTTS signals text file.

Plot the graph by clicking on the “To New Graph” button, or by the following:

Right Click on the file _ To New Graph

This is shown below:

Fig. 16. Right-click onthe file Dma-pet.txtand select ÒTo NewGraphÓ to plot thegraph.

If the data are generated by the DMA 2980 using tension, compression, or bendingclamps, then the moduli will be donoted by the letter “E”. If the data are generatedusing the shear sandwich clamp, then the moduli are denoted by the letter “G”.Data Analysis must be set up for the correct type of modulus to be shifted. This isdone by the following steps:

Graph _ Miscellaneous

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Fig. 17. Changing themodulus type in TTSData Analysis. Changethe modulus type(Oscillation labels)using the pull-downselector at the bottomo f t h e G r a p hMiscellaneous window.

→

The x-axis variable must be set to Frequency or Angular Frequency. To selectthe graph variables, use the following sequence:

Graph _ Change Variables

This brings up the following window, in which the desired x- and y-axes variablescan be selected:

Fig. 18. Screencapture of Graphvariables selectionwindow.. Up to 4 y-axis variables can beselected.

With Frequency on the x-axis and E’, storage modulus, as the y-axis variable, thegraph should look like the following:

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Fig. 19. Graph of TTSData before shifting.

Note that the frequency range is 0.1 to 20 Hz. It is not recommended that the graphkey be displayed because in most cases, it obstructs the view of the graph. Thegraph key can be hidden by going into:

Graph _ Key

or by pressing , and then, unchecking the “Displayed” option in the followingwindow:

Fig. 20. Disabling thekey display on thegraph.

Uncheck this

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Now, the TTS session has to be started by

TTS _ Begin Session

Once this is done, the greyed-out items under the TTS menu will become activated.The next step is to select a reference temperature. By selecting a reference curve,one essentially chooses a frequency scan at the temperature of interest. The curvethat is selected will remain unchanged, while all the other curves will be shiftedrelative to the reference curve. The frequency scan curves at temperatures higherthan the reference temperature will shift to the left along the frequency axis, i.e.,they will shift to lower frequencies or longer times. The lower temperature data willshift to the right of the reference curve (higher frequencies or shorter times). Toselect the reference curve, press button, or go to

TTS _ Set Reference Curve

This will bring up the following window in which, one can simply select thereference temperature (75°C in this example) and click the button.

Fig. 21. Selecting areferencetemperature,Tref=75¡C. →

Now that the reference temperature is selected, the curves can be shifted. To dothis, click on , or go to

TTS _ Shift Curves

The software will automatically move the curves relative to the reference curve, asshown below in Fig 21. The extended frequency range obtained by the TTS methodis 10

-13 to 10

18 Hz, an astounding 33 decade range! Hence, at 75°C, one is able to

ascertain the behavior of the PET sample at very short times (or high frequencies)and very long times (or low frequencies). This clearly demonstrates the power ofthe TTS method.

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Fig. 22. Shifted Curvesto a re fe rencetemperature of 75¡C.

Note that we have not generated a master curve or saved any shifting information sofar. In order to save the results so that it can be used later, one must create a mastercurve. The procedure for doing this is described in a later section.

The individual frequency scans can be manually dragged and shifted to fine-tune the mastercurve as per one’s liking. To do this, left-click on the frequency scan of choice in the graph,and keeping the mouse button pressed, drag the single scan to the left or right and release.In fact, for this example, the lowest temperature scan was shifted manually.

Analysis using WLF/Arrhenius Models

The amount of shift of a frequency scan that is associated with a particulartemperature will be different from that of a frequency scan associated with any othertemperature‡. Therefore, for every temperature, there is a certain characteristicshift-factor. There are some mathematical models that relate the temperatures to therespective shift-factors. The William-Landel-Ferry (WLF) equation is usually validfor materials from temperatures below Tg up to about Tg+100 °C [3]. Beyond this,an Arrhenius model is better suited.

When the TTS session is first begun, the software adds a file to the results file frameon the left. This file is usually called Graph and it contains the shift factor versustemperature information. After performing the curve-shifting, one can click on the

Graph file and, using the key, make a new graph of this data. It is a good ideato assess how well the data shifted by looking at the shift-factor versus temperaturedata and how well a model was able to fit it. For our example, the shift factorversus temperature curve looks like the following:

‡ See references if unfamiliar with shift-factor concepts.

Lower Temperature Data

Extended Frequency RangeExtended Frequency Range

Higher Temperature Data

InitialRange

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Fig. 23. Graph ofshift-factor versustemperature.

The WLF model will be used for fitting the above data because the test temperaturesare within the sub-Tg to Tg + 100°C range. To select the model on the software, goto

Analysis _ Model…

This will bring up the following window, in which one can select the WLF modelfrom the list, and click .

Fig. 24. Selecting theanalysis model forfitting shift-factors vstemperature data.

The next step is to select the range of data points to analyze. This can be done by

Analysis _ Limits

which will bring up the window shown below. In this example, we have opted toinclude all the data points, and hence, the “Whole Curve” option has been selected.One can select a limited range over which to fit any model by unchecking the “-Whole Curve” option and entering the data limits on the temperature scale.

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Fig. 25. Screencapture of the analysislimits window.

All that remains is to start the fitting session by going to

Analysis _ Go

This begins the fitting procedure using the WLF model and, when done, adds the fitto the graph, as shown below. The graph is also annotated with the fit parameterscharacteristic to the WLF equation, namely, C1 and C2, and the stardard error. Thestandard error of the fit is a good measure of the validity of the fit. Determinationof acceptable values of standard error is up to the user’s discretion. It isrecommended that the standard error be less than 20 for a good fit. One should notethat in some cases, the Arrhenius model may be more applicable in fitting the data,in which case, the standard error will be high if one tries to fit the WLF model. Ifthe material is not thermorheologically simple at all temperatures, one may observea high standard error.

All the above steps can be easily performed using the icons in the Analysis toolbar.

Fig. 26. The shiftf a c t o r s v e r s u stemperature and theWLF fit with the valuesof its parameters.

Model Selector

Data Range

“Go” – Begin Fitting

Delete All

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Generating the Master Curve

The purpose of generating a master curve is to put the data in a usable format. Oncethe master curve has been generated, all the data that existed as a fragmentedcomposite of individual frequency scans will be merged into a single file. To createa master curve, one should first display the graph with the shifted frequency sweepsfrom the Window menu. Then, by following the steps below, the master curve isgenerated:

TTS _ Generate Master Curve

The software adds this master curve as a new file in the list of opened files. Thisfilename of the master curve will be the same as the original text file, but with a“tts” suffix added. In our example, the filename is Dma-pet-txt tts. To savethe master curve, one should select the file using the mouse and perform

File _ Save (or Save As…)

The file will be saved with the extension *.rsl.

Fig. 27. The final EÕmaster curve at Tr =75¡C.

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References

[1] FERRY, J. D., “Viscoelastic Properties of Polymers”John Wiley & Sons, Inc., New York, NY, 1980ISBN 0-471-04894-1

[2] MCCRUM, N. G., READ, B. E., AND WILLIAMS , G., “Anelastic and DielectricEffects in Polymeric Solids”Dover Publications, Inc., New York, NY, 1991. (Copyright 1967 by John Wiley & Sons)ISBN 0-486-66752-9

[3] NIELSEN, L. E., AND LANDEL, R. F., “Mechanical Properties of Polymers andComposites” 2Ed.Marcel Dekker, Inc., New York, NY, 1994ISBN 0-8247-8964-4

[4] W ARD, I. M., AND HADLEY , D. W., “An Introduction to the MechanicalProperties of Solid Polymers”John Wiley & Sons Ltd., West Sussex, England, 1993ISBN 0-47193887-4